OpenRaiser/Intern-Atlas huggingface dataset:
An Error Probability Approach to MIMO Wiretap Channels
Venue: arXiv cs.IT 2013
Year: 2013

We consider MIMO (Multiple Input Multiple Output) wiretap channels, where a legitimate transmitter Alice is communicating with a legitimate receiver Bob in the presence of an eavesdropper Eve, and communication is done via MIMO channels. We suppose that Alice's strategy is to use a codebook which has a lattice structure, which then allows her to perform coset encoding. We analyze Eve's probability of correctly decoding the message Alice meant to Bob, and from minimizing this probability, we derive a code design criterion for MIMO lattice wiretap codes. The case of block fading channels is treated similarly, and fast fading channels are derived as a particular case. The Alamouti code is carefully studied as an illustration of the analysis provided.
On the Achievable DoF and User Scaling Law of Opportunistic Interference Alignment in 3-Transmitter MIMO Interference Channels
Venue: arXiv cs.IT 2013
Year: 2013

In this paper, we propose opportunistic interference alignment (OIA) schemes for three-transmitter multiple-input multiple-output (MIMO) interference channels (ICs). In the proposed OIA, each transmitter has its own user group and selects a single user who has the most aligned interference signals. The user dimensions provided by multiple users are exploited to align interfering signals. Contrary to conventional IA, perfect channel state information of all channel links is not required at the transmitter, and each user just feeds back one scalar value to indicate how well the interfering channels are aligned. We prove that each transmitter can achieve the same degrees of freedom (DoF) as the interference free case via user selection in our system model that the number of receive antennas is twice of the number of transmit antennas. Using the geometric interpretation, we find the required user scaling to obtain an arbitrary non-zero DoF. Two OIA schemes are proposed and compared with various user selection schemes in terms of achievable rate/DoF and complexity.
Distributed and Cascade Lossy Source Coding with a Side Information "Vending Machine"
Venue: arXiv cs.IT 2013
Year: 2013

Source coding with a side information "vending machine" is a recently proposed framework in which the statistical relationship between the side information and the source, instead of being given and fixed as in the classical Wyner-Ziv problem, can be controlled by the decoder. This control action is selected by the decoder based on the message encoded by the source node. Unlike conventional settings, the message can thus carry not only information about the source to be reproduced at the decoder, but also control information aimed at improving the quality of the side information. In this paper, the analysis of the trade-offs between rate, distortion and cost associated with the control actions is extended from the previously studied point-to-point set-up to two basic multiterminal models. First, a distributed source coding model is studied, in which two encoders communicate over rate-limited links to a decoder, whose side information can be controlled. The control actions are selected by the decoder based on the messages encoded by both source nodes. For this set-up, inner bounds are derived on the rate-distortion-cost region for both cases in which the side information is available causally and non-causally at the decoder. These bounds are shown to be tight under specific assumptions, including the scenario in which the sequence observed by one of the nodes is a function of the source observed by the other and the side information is available causally at the decoder. Then, a cascade scenario in which three nodes are connected in a cascade and the last node has controllable side information, is also investigated. For this model, the rate-distortion-cost region is derived for general distortion requirements and under the assumption of causal availability of side information at the last node.
Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the Cutset
Venue: arXiv cs.DS 2013
Year: 2013

Given a directed graph $G$, a set of $k$ terminals and an integer $p$, the \textsc{Directed Vertex Multiway Cut} problem asks if there is a set $S$ of at most $p$ (nonterminal) vertices whose removal disconnects each terminal from all other terminals. \textsc{Directed Edge Multiway Cut} is the analogous problem where $S$ is a set of at most $p$ edges. These two problems indeed are known to be equivalent. A natural generalization of the multiway cut is the \emph{multicut} problem, in which we want to disconnect only a set of $k$ given pairs instead of all pairs. Marx (Theor. Comp. Sci. 2006) showed that in undirected graphs multiway cut is fixed-parameter tractable (FPT) parameterized by $p$. Marx and Razgon (STOC 2011) showed that undirected multicut is FPT and directed multicut is W[1]-hard parameterized by $p$. We complete the picture here by our main result which is that both \textsc{Directed Vertex Multiway Cut} and \textsc{Directed Edge Multiway Cut} can be solved in time $2^{2^{O(p)}}n^{O(1)}$, i.e., FPT parameterized by size $p$ of the cutset of the solution. This answers an open question raised by Marx (Theor. Comp. Sci. 2006) and Marx and Razgon (STOC 2011). It follows from our result that \textsc{Directed Multicut} is FPT for the case of $k=2$ terminal pairs, which answers another open problem raised in Marx and Razgon (STOC 2011).
Synthesis and Optimization of Reversible Circuits - A Survey
Venue: arXiv cs.ET 2013
Year: 2013

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.
Robust Image Analysis by L1-Norm Semi-supervised Learning
Venue: arXiv cs.CV 2013
Year: 2013

This paper presents a novel L1-norm semi-supervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm Laplacian regularization is defined directly over the eigenvectors of the normalized Laplacian matrix, we successfully formulate semi-supervised learning as an L1-norm linear reconstruction problem which can be effectively solved with sparse coding. By working with only a small subset of eigenvectors, we further develop a fast sparse coding algorithm for our L1-norm semi-supervised learning. Due to the sparsity induced by sparse coding, the proposed algorithm can deal with the noise in the data to some extent and thus has important applications to robust image analysis, such as noise-robust image classification and noise reduction for visual and textual bag-of-words (BOW) models. In particular, this paper is the first attempt to obtain robust image representation by sparse co-refinement of visual and textual BOW models. The experimental results have shown the promising performance of the proposed algorithm.
The General Traveling Salesman Problem, Version 5
Venue: arXiv cs.DS 2013
Year: 2013

This paper is example 5 in chapter 5. Let H be an n-cycle. A permutation s is H-admissible if Hs = H' where H' is an n-cycle. Here we define a 19 X 19 matrix, M, in the following way: We obtain the remainders modulo 100 of each of the smallest 342 odd primes. we obtain the remainders modulo 100 of each of the primes. They are placed in M according to the original value of each prime. Thus their placement depends on the the original ordinal values of the primes according to size. We use this ordering to place the primes in M. Let H_0 be an initial 19 cycles arbitrarily chosen. We apply a sequence of up to [ln(n)+1] H_0 3-cycles to obtain a 19-cycle of smaller value than H_0, call the new 19-cycle H_1. We follow this procedure to obtain H_1. We call [ln(n)] + 1 a chain. We add up the values of the 19-cycles in each chain. This procedure continues until we cannot obtain a chain the sum of whose values is not negative. COMMENT. I've renamed the document "Yhe General Traveling Salesman Problem, Version 5". I preciously named it "The Traveling Salesman, Version 5". Although the algorithms work on the GTSP, I thought that more people would google it if it was named "The Traveling Salesman Problem." Rhar qas because my work is only available through arxiv.org,
A Reliable Effective Terascale Linear Learning System
Venue: arXiv cs.LG 2013
Year: 2013

We present a system and a set of techniques for learning linear predictors with convex losses on terascale datasets, with trillions of features, {The number of features here refers to the number of non-zero entries in the data matrix.} billions of training examples and millions of parameters in an hour using a cluster of 1000 machines. Individually none of the component techniques are new, but the careful synthesis required to obtain an efficient implementation is. The result is, up to our knowledge, the most scalable and efficient linear learning system reported in the literature (as of 2011 when our experiments were conducted). We describe and thoroughly evaluate the components of the system, showing the importance of the various design choices.
Understanding BitTorrent Through Real Measurements
Venue: arXiv cs.NI 2013
Year: 2013

In this paper the results of the BitTorrent measurement study are presented. Two sources of BitTorrent data were utilized: meta-data files that describe the content of resources shared by BitTorrent users and the logs of one of the currently most popular BitTorrent clients - μTorrent. μTorrent is founded upon a rather newly released UDP-based μTP protocol that is claimed to be more efficient than TCP-based clients. Experimental data have been collected for fifteen days from the popular torrent-discovery site thepiratebay.org (more than 30,000 torrents were captured and analyzed). During this period the activity and logs of an unmodified version of μTorrent client downloading sessions have been also captured. The obtained experimental results are swarm-oriented (not tracker-oriented as has been previously researched), which has allowed us to look at BitTorrent and its users from an exchanged resources perspective. Moreover, comparative analysis of the clients' connections with and without μTP protocol is carried out to verify to what extent μTP improves BitTorrent transmissions. To the authors' best knowledge, none of the previous studies have addressed these issues.
Multiuser Diversity in Interfering Broadcast Channels: Achievable Degrees of Freedom and User Scaling Law
Venue: arXiv cs.IT 2013
Year: 2013

This paper investigates how multiuser dimensions can effectively be exploited for target degrees of freedom (DoF) in interfering broadcast channels (IBC) consisting of K-transmitters and their user groups. First, each transmitter is assumed to have a single antenna and serve a singe user in its user group where each user has receive antennas less than K. In this case, a K-transmitter single-input multiple-output (SIMO) interference channel (IC) is constituted after user selection. Without help of multiuser diversity, K-1 interfering signals cannot be perfectly removed at each user since the number of receive antennas is smaller than or equal to the number of interferers. Only with proper user selection, non-zero DoF per transmitter is achievable as the number of users increases. Through geometric interpretation of interfering channels, we show that the multiuser dimensions have to be used first for reducing the DoF loss caused by the interfering signals, and then have to be used for increasing the DoF gain from its own signal. The sufficient number of users for the target DoF is derived. We also discuss how the optimal strategy of exploiting multiuser diversity can be realized by practical user selection schemes. Finally, the single transmit antenna case is extended to the multiple-input multiple-output (MIMO) IBC where each transmitter with multiple antennas serves multiple users.
Multi-Stage Complex Contagions
Venue: arXiv cs.SI 2013
Year: 2013

The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at different stages --- which could, for example, represent differing levels of support for a social movement or differing levels of commitment to a certain product or idea --- exert different amounts of influence on their neighbors. We demonstrate that the presence of even one additional stage introduces novel dynamical behavior, including interplay between multiple cascades, that cannot occur in single-stage contagion models. We find that cascades --- and hence collective action --- can be driven not only by high-stage influencers but also by low-stage influencers.
On Refined Versions of the Azuma-Hoeffding Inequality with Applications in Information Theory
Venue: arXiv cs.IT 2013
Year: 2013

This is a survey paper with some original results of the author on refined versions of the Azuma-Hoeffding inequality with some examples that are related to information theory. This work has evolved to the joint paper with Maxim Raginsky in arXiv:1212.4663v3.
Complexity of the path avoiding forbidden pairs problem revisited
Venue: arXiv cs.DM 2013
Year: 2013

Let G = (V, E) be a directed acyclic graph with two distinguished vertices s, t and let F be a set of forbidden pairs of vertices. We say that a path in G is safe, if it contains at most one vertex from each pair {u, v} in F. Given G and F, the path avoiding forbidden pairs (PAFP) problem is to find a safe s-t path in G. We systematically study the complexity of different special cases of the PAFP problem defined according to the mutual positions of forbidden pairs. Fix one topological ordering of vertices; we say that pairs {u, v} and {x, y} are disjoint, if u, v < x, y, nested, if u < x, y < v, and halving, if u < x < v < y. The PAFP problem is known to be NP-hard in general or if no two pairs are disjoint; we prove that it remains NP-hard even when no two forbidden pairs are nested. On the other hand, if no two pairs are halving, the problem is known to be solvable in cubic time. We simplify and improve this result by showing an O(M(n)) time algorithm, where M(n) is the time to multiply two n \times n boolean matrices.
Integer Feasibility of Random Polytopes
Venue: arXiv cs.DS 2013
Year: 2013

We study integer programming instances over polytopes P(A,b)={x:Ax<=b} where the constraint matrix A is random, i.e., its entries are i.i.d. Gaussian or, more generally, its rows are i.i.d. from a spherically symmetric distribution. The radius of the largest inscribed ball is closely related to the existence of integer points in the polytope. We show that for m=2^O(sqrt{n}), there exist constants c_0 < c_1 such that with high probability, random polytopes are integer feasible if the radius of the largest ball contained in the polytope is at least c_1sqrt{log(m/n)}; and integer infeasible if the largest ball contained in the polytope is centered at (1/2,...,1/2) and has radius at most c_0sqrt{log(m/n)}. Thus, random polytopes transition from having no integer points to being integer feasible within a constant factor increase in the radius of the largest inscribed ball. We show integer feasibility via a randomized polynomial-time algorithm for finding an integer point in the polytope. Our main tool is a simple new connection between integer feasibility and linear discrepancy. We extend a recent algorithm for finding low-discrepancy solutions (Lovett-Meka, FOCS '12) to give a constructive upper bound on the linear discrepancy of random matrices. By our connection between discrepancy and integer feasibility, this upper bound on linear discrepancy translates to the radius lower bound that guarantees integer feasibility of random polytopes.
Memoryless computation: new results, constructions, and extensions
Venue: arXiv cs.CC 2013
Year: 2013

In this paper, we are interested in memoryless computation, a modern paradigm to compute functions which generalises the famous XOR swap algorithm to exchange the contents of two variables without using a buffer. This uses a combinatorial framework for procedural programming languages, where programs are only allowed to update one variable at a time. We first consider programs which do not have any memory. We prove that any function of $n$ variables can be computed this way in only $4n-3$ variable updates. We then derive the exact number of instructions required to compute any manipulation of variables. This shows that combining variables, instead of simply moving them around, not only allows for memoryless programs, but also yields shorter programs. Second, we show that allowing programs to use memory is also incorporated in the memoryless computation framework. We then quantify the gains obtained by using memory: this leads to shorter programs and allows us to use only binary instructions, which is not sufficient in general when no memory is used.
Learning with Submodular Functions: A Convex Optimization Perspective
Venue: arXiv cs.LG 2013
Year: 2013

Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful set of regularization functions for supervised and unsupervised learning. In this monograph, we present the theory of submodular functions from a convex analysis perspective, presenting tight links between certain polyhedra, combinatorial optimization and convex optimization problems. In particular, we show how submodular function minimization is equivalent to solving a wide variety of convex optimization problems. This allows the derivation of new efficient algorithms for approximate and exact submodular function minimization with theoretical guarantees and good practical performance. By listing many examples of submodular functions, we review various applications to machine learning, such as clustering, experimental design, sensor placement, graphical model structure learning or subset selection, as well as a family of structured sparsity-inducing norms that can be derived and used from submodular functions.
Efficient Discovery of Association Rules and Frequent Itemsets through Sampling with Tight Performance Guarantees
Venue: arXiv cs.DS 2013
Year: 2013

The tasks of extracting (top-$K$) Frequent Itemsets (FI's) and Association Rules (AR's) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running time is hindered by the need of scanning the entire dataset, possibly multiple times. High quality approximations of FI's and AR's are sufficient for most practical uses, and a number of recent works explored the application of sampling for fast discovery of approximate solutions to the problems. However, these works do not provide satisfactory performance guarantees on the quality of the approximation, due to the difficulty of bounding the probability of under- or over-sampling any one of an unknown number of frequent itemsets. In this work we circumvent this issue by applying the statistical concept of \emph{Vapnik-Chervonenkis (VC) dimension} to develop a novel technique for providing tight bounds on the sample size that guarantees approximation within user-specified parameters. Our technique applies both to absolute and to relative approximations of (top-$K$) FI's and AR's. The resulting sample size is linearly dependent on the VC-dimension of a range space associated with the dataset to be mined. The main theoretical contribution of this work is a proof that the VC-dimension of this range space is upper bounded by an easy-to-compute characteristic quantity of the dataset which we call \emph{d-index}, and is the maximum integer $d$ such that the dataset contains at least $d$ transactions of length at least $d$ such that no one of them is a superset of or equal to another. We show that this bound is strict for a large class of datasets.
A geometric analysis of subspace clustering with outliers
Venue: arXiv cs.IT 2013
Year: 2013

This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information about their dimensions. We develop a novel geometric analysis of an algorithm named sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, 2009. CVPR 2009 (2009) 2790-2797. IEEE], which significantly broadens the range of problems where it is provably effective. For instance, we show that SSC can recover multiple subspaces, each of dimension comparable to the ambient dimension. We also prove that SSC can correctly cluster data points even when the subspaces of interest intersect. Further, we develop an extension of SSC that succeeds when the data set is corrupted with possibly overwhelmingly many outliers. Underlying our analysis are clear geometric insights, which may bear on other sparse recovery problems. A numerical study complements our theoretical analysis and demonstrates the effectiveness of these methods.
On the Complexity of the Generalized MinRank Problem
Venue: arXiv cs.SC 2013
Year: 2013

We study the complexity of solving the \emph{generalized MinRank problem}, i.e. computing the set of points where the evaluation of a polynomial matrix has rank at most $r$. A natural algebraic representation of this problem gives rise to a \emph{determinantal ideal}: the ideal generated by all minors of size $r+1$ of the matrix. We give new complexity bounds for solving this problem using Gröbner bases algorithms under genericity assumptions on the input matrix. In particular, these complexity bounds allow us to identify families of generalized MinRank problems for which the arithmetic complexity of the solving process is polynomial in the number of solutions. We also provide an algorithm to compute a rational parametrization of the variety of a 0-dimensional and radical system of bi-degree $(D,1)$. We show that its complexity can be bounded by using the complexity bounds for the generalized MinRank problem.
New lower bounds for the border rank of matrix multiplication
Venue: arXiv cs.CC 2013
Year: 2013

The border rank of the matrix multiplication operator for n by n matrices is a standard measure of its complexity. Using techniques from algebraic geometry and representation theory, we show the border rank is at least 2n^2-n. Our bounds are better than the previous lower bound (due to Lickteig in 1985) of 3/2 n^2+ n/2 -1 for all n>2. The bounds are obtained by finding new equations that bilinear maps of small border rank must satisfy, i.e., new equations for secant varieties of triple Segre products, that matrix multiplication fails to satisfy.